Definition of Linear System
A system is considered linear if for any constants a, b that exist within the complex domain and for any inputs $ x_1(t)\! $ and $ x_{2}(t)\! $ yielding outputs $ y_{1}(t)\! $ and $ y_2(t)\! $ respectively, the response to $ x_1(t) + bx_{2}(t)\! $ is $ y_1(t) + by_{2}(t)\! $
This is saying that if i have 2 inputs of x(t) and y(t) and put them through a system, then multiply the 2 outputs by a constant, and add them together to get my final signal i should get the same if i multiply the two input signals by the constant first and add them, then send them through the system.
x(t) $ \to\! $ (system) $ \to\! $ *a $ \to\! $
.....................(sum) $ \to\! $ z(t)
y(t) $ \to\! $ (system) $ \to\! $ *b $ \to\! $
